Title: Exceptional jumps of Picard rank of K3 surfaces over number fields
Abstract:
Given a K3 surface X over a number field K, we prove that the
set of primes of K where the geometric Picard rank jumps is infinite,
assuming that X has everywhere potentially good reduction.
This result is formulated in the general framework of GSpin Shimura varieties and
I will explain other applications to abelian surfaces.
I will also discuss applications to the existence of rational curves on K3 surfaces.
The results in this talk are joint work with Ananth Shankar, Arul Shankar and Yunqing Tang.